A good question as to when guns were first chambered to 2 3/4". I have a circa 1880's Jeffery hammer live pigeon gun with original 2 3/4" chambers. Nothing on the proof marks to indicate this but a small 2 3/4" mark was stamped onto the forend fastener of the barrels. It was black powder proof and I have since had it proofed for nitro.
The Proof House in Birmingham may be able to answer your question on that.
Cost of submission for proof is a little over 20 per barrel. The real cost comes in with preparation, if any is required, as it would be rejected at the 'View' stage if the gun is off face, has any pitting or is defective in any way. From America the cost of shipping both ways is an expensive consideration too. Lagopus.....